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Fast Fourier transforms for nonequispaced data: A tutorial
, 2000
"... In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity o ..."
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Cited by 141 (31 self)
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In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFTalgorithms with respect to roundoff errors and apply NDFTalgorithms for the fast computation of Bessel transforms.
New Fourier reconstruction algorithms for computerized tomography
"... In this paper, we propose two new algorithms for high quality Fourier reconstructions of digital N × N images from their Radon transform. Both algorithms are based on fast Fourier transforms for nonequispaced data (NFFT) and require only O(N²log N) arithmetic operations. While the ..."
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Cited by 12 (3 self)
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In this paper, we propose two new algorithms for high quality Fourier reconstructions of digital N &times; N images from their Radon transform. Both algorithms are based on fast Fourier transforms for nonequispaced data (NFFT) and require only O(N&sup2;log N) arithmetic operations. While the rst algorithm includes a bivariate NFFT on the polar grid, the second algorithm consists of several univariate NFFTs on the socalled linogram.
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"... Abstract. In this paper, we propose a new linogram algorithm for the high quality Fourier reconstruction of digital N \Theta N images from their Radon transform. The algorithm is based on univariate fast Fourier transforms for nonequispaced data in the time domain and in the frequency domain. The al ..."
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Abstract. In this paper, we propose a new linogram algorithm for the high quality Fourier reconstruction of digital N \Theta N images from their Radon transform. The algorithm is based on univariate fast Fourier transforms for nonequispaced data in the time domain and in the frequency domain. The algorithm requires only O(N 2 log N) arithmetic operations and preserves the good reconstruction quality of the filtered backprojection. 1991 Mathematics Subject Classification. 44A12, 65T50 Key words and phrases. Fast Fourier transform for nonequispaced data, Radon transform, computerized tomography, gridding, linogram, chirpz transform 1 Introduction We are interested in efficient and high quality reconstructions of digital N \Theta N medical images from their Radon transform. The standard reconstruction algorithm, the filtered backprojection, ensures a good quality of the images at the expense of O(N
Let
"... ABSTRACT In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic co ..."
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ABSTRACT In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFT{algorithms with respect to roundo errors and apply NDFT{
and
"... Abstract. In this paper, we propose a new linogram algorithm for the high quality Fourier reconstruction of digital N N images from their Radon transform. The algorithm is based on univariate fast Fourier transforms for nonequispaced data in the time domain and in the frequency domain. The algorithm ..."
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Abstract. In this paper, we propose a new linogram algorithm for the high quality Fourier reconstruction of digital N N images from their Radon transform. The algorithm is based on univariate fast Fourier transforms for nonequispaced data in the time domain and in the frequency domain. The algorithm requires only O(N 2 logN) arithmetic operations and preserves the good reconstruction quality of the ltered backprojection. 1991 Mathematics Subject Classication. 44A12, 65T50 Key words and phrases. Fast Fourier transform for nonequispaced data, Radon transform, computerized tomography, gridding, linogram, chirp{z transform 1